Cordless telephones are well known, see, for example, "Funkschau", 1984, issue 17, page 16, which include a base station and associated hand sets. Each of the hand sets has a rod antenna. The rod antenna, projecting from the respective hand sets, is inconvenient in handling and distracting in appearance, and for storage, particularly on a temporary basis. It is also necessary to provide a transmit/receive (T/R) switch to permit duplex operation. The referenced application Ser. No. 06/571,078, of Jan. 16, 1984, Erat, now U.S. Pat. No. 4,590,614, describes an antenna which defines a dipole structure, formed by conductors located on a printed circuit board which is subdivided into two sections, the conductors on the printed circuit board on the respective sections being interconnected by high-resistance resistors or high-frequency chokes. The regions or zones on the printed circuit board, thus, form the dipole. The conductors or conductive surfaces may carry additional electrical structural components and units, such as integrated circuits, active and passive components, and the like.